The fate of Obamacare, gay marriage and other key cases rests with the straitlaced Sacramento native and his pragmatic take on the Constitution

At 6 a.m. in the Northern Virginia suburbs of Washington, when some Pentagon brass and White House aides are just rolling out of bed, Justice Anthony Kennedy is dressed in a well-cut suit and rolling down the driveway of his modest home. He is cautious at the wheel. Even when the streets and highways are empty, Kennedy obeys traffic laws. "He would never cross the street against a red light," says a former colleague. He arrives 30 minutes later at the imposing marble temple across the street from the Capitol. Designed to appear as ancient as democracy itself even though it...